2 Outline Applications Overview of Combustion Modeling Capabilities Chemical KineticsGas Phase Combustion ModelsDiscrete Phase ModelsPollutant ModelsCombustion Simulation Guidelines
3 ApplicationsWide range of homogeneous and heterogeneous reacting flowsFurnacesBoilersProcess heatersGas turbinesRocket enginesPredictions of:Flow field and mixing characteristicsTemperature fieldSpecies concentrationsParticulates and pollutantsTemperature in a gas furnaceCO2 mass fractionStream function
4 Aspects of Combustion Modeling Combustion ModelsDispersed Phase ModelsPremixedPartially premixedNonpremixedDroplet/particle dynamicsHeterogeneous reactionDevolatilizationEvaporationGoverning Transport EquationsMassMomentum (turbulence)EnergyChemical SpeciesRadiative Heat Transfer ModelsPollutant Models
5 Combustion Models Available in FLUENT Gas phase combustionGeneralized finite rate formulation (Magnussen model)Conserved scalar PDF model (one and two mixture fractions)Laminar flamelet model (V5)Zimont model (V5)Discrete phase modelTurbulent particle dispersionStochastic trackingParticle cloud model (V5)Pulverized coal and oil spray combustion submodelsRadiation models: DTRM, P-1, Rosseland and Discrete Ordinates (V5)Turbulence models: k-, RNG k-, RSM, Realizable k- (V5) and LES (V5)Pollutant models: NOx with reburn chemistry (V5) and soot
6 Modeling Chemical Kinetics in Combustion ChallengingMost practical combustion processes are turbulentRate expressions are highly nonlinear; turbulence-chemistry interactions are importantRealistic chemical mechanisms have tens of species, hundreds of reactions and stiff kinetics (widely disparate time scales)Practical approachesReduced chemical mechanismsFinite rate combustion modelDecouple reaction chemistry from turbulent flow and mixingMixture fraction approachesEquilibrium chemistry PDF modelLaminar flameletProgress variableZimont model
7 Generalized Finite Rate Model Chemical reaction process described using global mechanism.Transport equations for species are solved.These equations predict local time-averaged mass fraction, mj , of each species.Source term (production or consumption) for species j is net reaction rate over all k reactions in mechanism:Rjk (rate of production/consumption of species j in reaction k) is computed to be the smaller of the Arrhenius rate and the mixing or “eddy breakup” rate.Mixing rate related to eddy lifetime, k /.Physical meaning is that reaction is limited by the rate at which turbulence can mix species (nonpremixed) and heat (premixed).
8 Setup of Finite Rate Chemistry Models Requires:List of species and their propertiesList of reactions and reaction ratesFLUENT V5 provides this info in a mixture material database.Chemical mechanisms and physical properties for the most common fuels are provided in database.If you have different chemistry, you can:Create new mixtures.Modify properties/reactions of existing mixtures.
9 Generalized Finite Rate Model: Summary Advantages:Applicable to nonpremixed, partially premixed, and premixed combustionSimple and intuitiveWidely usedDisadvantages:Unreliable when mixing and kinetic time scales are comparable (requires Da >>1).No rigorous accounting for turbulence-chemistry interactionsDifficulty in predicting intermediate species and accounting for dissociation effects.Uncertainty in model constants, especially when applied to multiple reactions.
10 Conserved Scalar (Mixture Fraction) Approach: The PDF Model Applies to nonpremixed (diffusion) flames onlyAssumes that reaction is mixing-limitedLocal chemical equilibrium conditions prevail.Composition and properties in each cell defined by extent of turbulent mixing of fuel and oxidizer streams.Reaction mechanism is not explicitly defined by you.Reacting system treated using chemical equilibrium calculations (prePDF).Solves transport equations for mixture fraction and its variance, rather than species transport equations.Rigorous accounting of turbulence-chemistry interactions.
11 Mixture Fraction Definition The mixture fraction, f, can be written in terms of elemental mass fractions as:where Zk is the elemental mass fraction of some element, k. Subscripts F and O denote fuel and oxidizer inlet stream values, respectively.For simple fuel/oxidizer systems, the mixture fraction represents the fuel mass fraction in a computational cell.Mixture fraction is a conserved scalar:Reaction source terms are eliminated from governing transport equations.
12 Systems That Can be Modeled Using a Single Mixture Fraction Fuel/air diffusion flame:Diffusion flame with oxygen-enriched inlets:System using multiple fuel inlets:60% CH4 40% COf = 121% O2 79% N2f = 035% O2 65% N2f = 060% CH4 40% COf = 135% O2 65% N2f = 060% CH4 20% CO 10% C3H8 10% CO2f = 121% O2 79% N2f = 060% CH4 20% CO 10% C3H8 10% CO2f = 1
13 Equilibrium Approximation of System Chemistry Chemistry is assumed to be fast enough to achieve equilibrium.Intermediate species are included.
14 PDF Modeling of Turbulence-Chemistry Interaction Fluctuating mixture fraction is completely defined by its probability density function (PDF).p(V), the PDF, represents fraction of sampling time when variable, V, takes a value between V and V + V.p(f) can be used to compute time-averaged values of variables that depend on the mixture fraction, f:Species mole fractionsTemperature, density
15 PDF Model Flexibility Nonadiabatic systems: Second conserved scalar: In real problems, with heat loss or gain, local thermo-chemical state must be related to mixture fraction, f, and enthalpy, h.Average quantities now evaluated as a function of mixture fraction, enthalpy (normalized heat loss/gain), and the PDF, p(f).Second conserved scalar:With second scalar in FLUENT, you can model:Two fuel streams with different compositions and single oxidizer stream (visa versa)Nonreacting stream in addition to a fuel and an oxidizerCo-firing a gaseous fuel with another gaseous, liquid, or coal fuelFiring single coal with two off-gases (volatiles and char burnout products) tracked separately
16 Mixture Fraction/PDF Model: Summary Advantages:Predicts formation of intermediate species.Accounts for dissociation effects.Accounts for coupling between turbulence and chemistry.Does not require the solution of a large number of species transport equationsRobust and economicalDisadvantages:System must be near chemical equilibrium locally.Cannot be used for compressible or non-turbulent flows.Not applicable to premixed systems.
17 The Laminar Flamelet Model Extension of the mixture fraction PDF model to moderate chemical nonequilibriumTurbulent flame modeled as an ensemble of stretched laminar, opposed flow diffusion flamesTemperature, density and species (for adiabatic) specified by two parameters, the mixture fraction and scalar dissipation rateRecall that for the mixture fraction PDF model (adiabatic), thermo-chemical state is function of f onlyc can be related to the local rate of strain
18 Laminar Flamelet Model (2) Statistical distribution of flamelet ensemble is specified by the PDF P(f,c), which is modeled as Pf (f) Pc (c), with a Beta function for Pf (f) and a Dirac-delta distribution for Pc (c)Only available for adiabatic systems in V5Import strained flame calculationsprePDF or Sandia’s OPPDIF codeSingle or multiple flameletsSingle: user specified strain, aMultiple: strained flamelet library, 0 < a < aextinctiona=0 equilibriuma= aextinction is the maximum strain rate before flame extinguishesPossible to model local extinction pockets (e.g. lifted flames)
19 The Zimont Model for Premixed Combustion Thermo-chemistry described by a single progress variable,Mean reaction rate,Turbulent flame speed, Ut, derived for lean premixed combustion and accounts forEquivalence ratio of the premixed fuelFlame front wrinkling and thickening by turbulenceFlame front quenching by turbulent stretchingDifferential molecular diffusionFor adiabatic combustion,The enthalpy equation must be solved for nonadiabatic combustion
20 Discrete Phase ModelTrajectories of particles/droplets/bubbles are computed in a Lagrangian frame.Exchange (couple) heat, mass, and momentum with Eulerian frame gas phaseDiscrete phase volume fraction must < 10%Although the mass loading can be largeNo particle-particle interaction or break upTurbulent dispersion modeled byStochastic trackingParticle cloud (V5)Rosin-Rammler or linear size distributionParticle tracking in unsteady flows (V5)Model particle separation, spray drying, liquid fuel or coal combustion, etc.Continuous phase flow field calculationParticle trajectory calculationUpdate continuous phase source terms
21 Particle Dispersion: The Stochastic Tracking Model Turbulent dispersion is modeled by an ensemble of Monte-Carlo realizations (discrete random walks)Particles convected by the mean velocity plus a random direction turbulent velocity fluctuationEach trajectory represents a group of particles with the same properties (initial diameter, density etc.)Turbulent dispersion is important becausePhysically realistic (but computationally more expensive)Enhances stability by smoothing source terms and eliminating local spikes in coupling to the gas phaseCoal particle tracks in an industrial boiler
22 Particle Dispersion: The Particle Cloud Model Track mean particle trajectory along mean velocityAssuming a 3D multi-variate Gaussian distribution about this mean track, calculate particle loading within three standard deviationsRigorously accounts for inertial and drift velocitiesA particle cloud is required for each particle type (e.g. initial d,r etc.)Particles can escape, reflect or trap (release volatiles) at wallsEliminates (single cloud) or reduces (few clouds) stochastic trackingDecreased computational expenseIncreased stability since distributed source terms in gas phaseBUT decreased accuracy sinceGas phase properties (e.g. temperature) are averaged within cloudPoor prediction of large recirculation zones
23 Particle Tracking in Unsteady Flows Each particle advanced in time along with the flowFor coupled flows using implicit time stepping, sub-iterations for the particle tracking are performed within each time stepFor non-coupled flows or coupled flows with explicit time stepping, particles are advanced at the end of each time step
24 Coal/Oil Combustion Models Coal or oil combustion modeled by changing the modeled particle toDroplet - for oil combustionCombusting particle - for coal combustionSeveral devolatilization and char burnout models provided.Note: These models control the rate of evolution of the fuel off-gas from coal/oil particles. Reactions in the gas (continuous) phase are modeled with the PDF or finite rate combustion model.
25 NOx Models NOx consists of mostly nitric oxide (NO). Precursor for smogContributes to acid rainCauses ozone depletionThree mechanisms included in FLUENT for NOx production:Thermal NOx - Zeldovich mechanism (oxidation of atmospheric N)Most significant at high temperaturesPrompt NOx - empirical mechanisms by De Soete, Williams, etc.Contribution is in general smallSignificant at fuel rich zonesFuel NOx - Empirical mechanisms by De Soete, Williams, etc.Predominant in coal flames where fuel-bound nitrogen is high and temperature is generally low.NOx reburn chemistry (V5)NO can be reduced in fuel rich zones by reaction with hydrocarbons
26 Soot modeling in FLUENT Two soot formation models are available:One-step model (Khan and Greeves)Single transport equation for soot mass fractionTwo-Step model (Tesner)Transport equations for radical nuclei and soot mass fraction concentrationsSoot formation modeled by empirical rate constantswhere, C, pf, and F are a model constant, fuel partial pressure and equivalence ratio, respectivelySoot combustion (destruction) modeled by Magnussen modelSoot affects the radiation absorptionEnable Soot-Radiation option in the Soot panel
27 Combustion Guidelines and Solution Strategies Start in 2DDetermine applicability of model physicsMesh resolution requirements (resolve shear layers)Solution parameters and convergence settingsBoundary conditionsCombustion is often very sensitive to inlet boundary conditionsCorrect velocity and scalar profiles can be criticalWall heat transfer is challenging to predict; if known, specify walltemperature instead of external convection/radiation BCInitial conditionsWhile steady-state solution is independent of the IC, poor IC may cause divergence due to the number and nonlinearity of the transport equationsCold flow solution, then gas combustion, then particles, then radiationFor strongly swirling flows, increase the swirl gradually
28 Combustion Guidelines and Solution Strategies (2) Underrelaxation FactorsThe effect of under-relaxation is highly nonlinearDecrease the diverging residual URF in increments of 0.1Underrelax density when using the mixture fraction PDF model (0.5)Underrelax velocity for high bouyancy flowsUnderrelax pressure for high speed flowsOnce solution is stable, attempt to increase all URFs to as close to defaults as possible (and at least 0.9 for T, P-1, swirl and species (or mixture fraction statistics))DiscretizationStart with first order accuracy, then converge with second order to improve accuracySecond order discretization especially important for tri/tet meshesDiscrete Phase Model - to increase stability,Increase number of stochastic tracks (or use particle cloud model)Decrease DPM URF and increase number of gas phase iterations per DPM
29 Combustion Guidelines and Solution Strategies (3) Magnussen modelDefaults to finite rate/eddy-dissipation (Arrhenius/Magnussen)For nonpremixed (diffusion) flames turn off finite ratePremixed flames require Arrhenius term so that reactants don’t burn prematurelyMay require a high temperature initialization/patchUse temperature dependent Cp’s to reduce unrealistically high temperaturesMixture fraction PDF modelModel of choice if underlying assumptions are validUse adequate numbers of discrete points in look up tables to ensure accurate interpolation (no affect on run-time expense)Use beta PDF shape
30 Combustion Guidelines and Solution Strategies (4) TurbulenceStart with standard k-e modelSwitch to RNG k-e , Realizable k-e or RSM to obtain better agreement with data and/or to analyze sensitivity to the turbulence modelJudging ConvergenceResiduals should be less than 10-3 except for T, P-1 and species, which should be less than 10-6The mass and energy flux reports must balanceMonitor variables of interest (e.g. mean temperature at the outlet)Ensure contour plots of field variables are smooth, realistic and steady
31 Concluding RemarksFLUENT V5 is the code of choice for combustion modeling.Outstanding set of physical modelsMaximum convenience and ease of useBuilt-in database of mechanisms and physical propertiesGrid flexibility and solution adaptionA wide range of reacting flow applications can be addressed by the combustion models in FLUENT.Make sure the physical models you are using are appropriate for your application.